Solskjaer dodged questions about their apparent interest in Sporting CP midfielder Bruno Fernandes, while the likes of Kalidou Koulibaly, James Maddison and Jack Grealish have also been linked with a January move to Old Trafford. The Red Devils are looking at an offer of around £50 million-plus add-ons (h/t The Daily Mail) for the Portugal worldwide who scored twice in Sporting's 3-1 win against Vitoria on Saturday night.
Speaking after the victory at Setubal, he said: "I can't guarantee any of these things because I don't know".
'I don't like to think about that, but I will think about alternatives in case Bruno leaves.
"I can only say that we are working really well to improve the squad".
With Paul Pogba and Scott McTominay facing prolonged periods of absence, United have been heavily linked with a move for Portugal worldwide midfielder Fernandes and officials from the two clubs are said to have been in talks on Friday.
They remain short up front after allowing Romelu Lukaku and Alexis Sanchez to leave the club last summer. They didn't accept a deal with Tottenham for 70m euros but that would have been paid with 40m euros upfront and then another 30m.
Ahead of Manchester United's match against Norwich City this weekend, Solskjaer was asked about his relationship with the club's executive vice-chairman and if he gets enough of a say in their immediate transfer plans.
"I have those conversations with Ed all the time and we are looking at how we are going to look in one month's time, five months' time, in the longer period. I hope it doesn't happen but in Portugal, unfortunately we can not hold on to our best players for very long and he is the best player in the league", Sporting coach Silas said recently.